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SelfSupervised Video Forensics by AudioVisual Anomaly Detection ; Manipulated videos often contain subtle inconsistencies between their visual and audio signals. We propose a video forensics method, based on anomaly detection, that can identify these inconsistencies, and that can be trained solely using real, unlabeled data. We train an autoregressive model to generate sequences of audiovisual features, using feature sets that capture the temporal synchronization between video frames and sound. At test time, we then flag videos that the model assigns low probability. Despite being trained entirely on real videos, our model obtains strong performance on the task of detecting manipulated speech videos. Project site httpscfeng16.github.ioaudiovisualforensics |
Double scaling limit of the prismatic tensor model ; In S. Giombi, I. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, it Phys. Rev. bf D 98 2018 10, 105005, a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using the intermediate field method. We explicitly exhibit the nexttoleading order Feynman graphs in the 1N expansion. Using appropriate combinatorial tools, we further study the general term of the 1N expansion and we compute the 2point function in the double scaling limit. |
OPDNL4Opt An ensemble approach for the NER task of the optimization problem ; In this paper, we present an ensemble approach for the NL4Opt competition subtask 1NER task. For this task, we first fine tune the pretrained language models based on the competition dataset. Then we adopt differential learning rates and adversarial training strategies to enhance the model generalization and robustness. Additionally, we use a model ensemble method for the final prediction, which achieves a microaveraged F1 score of 93.3 and attains the second prize in the NER task. |
The singularities of Selberg and DotsenkoFateevlike integrals ; We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3point and 4point functions of BPZ's minimal models of 2D CFT as described by Felder and Silvotti and Dotsenko and Fateev the Coulomb gas formalism''. This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric as in the Selberg integral itself or, more generally, what we call DFsymmetric,'' we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods. |
Pair production of heavy quarkonia in the color evaporation model ; In the article, we study pair production of heavy quarkonia Jpsi Jpsi, UpsilonUpsilon, Upsilon Jpsi in the improved color evaporation model via the parton Reggeization approach. The last one is based on highenergy factorization of hard processes in multiRegge kinematics, the KimberMartinRyskinWatt model for unintegrated parton distribution functions, and the Lipatov effective field theory of Reggezied gluons and quarks. We compare contributions from the single and double parton scattering mechanisms in the pair production of heavy quarkonia. The numerical calculations are performed with the MonteCarlo event generator KaTie. |
Altruism in Coalition Formation Games ; Nguyen et al. 1 introduced altruistic hedonic games in which agents' utilities depend not only on their own preferences but also on those of their friends in the same coalition. We propose to extend their model to coalition formation games in general, considering also the friends in other coalitions. Comparing our model to altruistic hedonic games, we argue that excluding some friends from the altruistic behavior of an agent is a major disadvantage that comes with the restriction to hedonic games. After introducing our model and showing some desirable properties, we additionally study some common stability notions and provide a computational analysis of the associated verification and existence problems. |
Topological Quantum Dimers Emerging from Kitaev Spin Liquid Bilayer Anyon Condensation Transition ; We present a bilayer spin model that illuminates the mechanism of topological anyon condensation transition. Our model harbors two distinct topological phases, Kitaev spin liquid bilayer state and resonating valence bond RVB state connected by a continuous transition. We show that the transition occurs by anyon condensation, and the hardcore dimer constraint of the RVB state plays a role of the order parameter. This model study offers an intuitive picture for anyon condensation transition, and is broadly applicable to generic tricoordinated lattices preserving the emergence of the RVB state from the Kitaev bilayer. |
Kittel's molecular zipper model on Cayley trees ; Kittel's 1D model represents a natural DNA with two strands as a molecular zipper, which may separated as the temperature is varied. We define multidimensional version of this model on a Cayley tree and study the set of Gibbs measures. We reduce description of Gibbs measures to solving of a nonlinear functional equation, with unknown functions called boundary laws defined on vertices of the Cayley tree. Each boundary law defines a Gibbs measure. We give general formula of free energy depending on the boundary law. Moreover, we find some concrete boundary laws and corresponding Gibbs measures. Explicit critical temperature for occurrence a phase transition nonuniqueness of Gibbs measures is obtained. |
Dark Sector Showers in the Lund Jet Plane ; We investigate the consequences of models where dark sector quarks could be produced at the LHC, which subsequently undergo a dark parton shower, generating jets of dark hadrons that ultimately decay back to Standard Model hadrons. This yields collider objects that can be nearly indistinguishable from Standard Model jets, motivating the reliance on substructure observables to tease out the signal. However, substructure predictions are sensitive to the details of the incalculable dark hadronization. We show that the Lund jet plane provides a very effective tool for designing observables that are resilient against the unknown impact of dark hadronization on the substructure properties of dark sector jets. |
Study of Compact Stars with Buchdahl Potential in 5D EinsteinGaussBonnet Gravity ; In this paper, we have presented a compact object model in the framework of EinsteinGaussBonnet gravity EGB with a linear equation of state considering a metric potential proposed for Buchdahl 1959. The new obtained models satisfy all physical requirements of a physically reasonable stellar object. We analyzed the effect of the GaussBonnet coupling constant alpha on the main physical characteristics of the model. We checked that the radial pressure, energy density and anisotropy are well defined and are regular in the interior of the star and are dependent of the values of the coupling constant. |
Modeling Nondeterministic Human Behaviors in Discrete Food Choices ; We establish a nondeterministic model that predicts a user's food preferences from their demographic information. Our simulator is based on NHANES dataset and domain expert knowledge in the form of established behavioral studies. Our model can be used to generate an arbitrary amount of synthetic datapoints that are similar in distribution to the original dataset and align with behavioral science expectations. Such a simulator can be used in a variety of machine learning tasks and especially in applications requiring human behavior prediction. |
A FourParameter BlackHole Solution in the Bumblebee Gravity Model ; The bumblebee gravity model includes a class of vectortensor theories of gravitation where the vector field couples to the Ricci tensor quadratically. We obtain an analytical spherical blackhole solution in this model. The solution has four parameters, expanding the twoparameter solution family known in the literature. Special choices of the parameters are pointed out and discussed. |
A4based model with linear seesaw scheme for lepton mass and mixing ; We suggest a lowscale model based on A4times Z4 times Z2 symmetry and a global lepton number U1L symmetry capable of generating the current neutrino data. The neutrino mass smallness is reproduced by the linear seesaw mechanism. The model can explain the current observed pattern of lepton mixing in which the reactor and atmospheric angles get the bestfit values, and the solar angle and Dirac phase lie within 3sigma limits. The obtained values of the sum of neutrino mass and the effective neutrino mass are below the present experimental limits. |
Sensitivity analysis for incomplete data via unmeasured confounding ; We present a method to analyze sensitivity of frequentist inferences to potential nonignorability of the missingness mechanism. Rather than starting from the selection model, as is typical in such analyses, we assume that the missingness arises through unmeasured confounding. Our model permits the development of measures of sensitivity that are analogous to those for unmeasured confounding in observational studies. We define an index of sensitivity, denoted MinNI, to be the minimum degree of nonignorability needed to change the mean value of the estimate of interest by a designated amount. We apply our model to sensitivity analysis for a proportion, but the idea readily generalizes to more complex situations. |
On the algebraic approach to GUP in anisotropic space ; Motivated by current searches for signals of Lorentz symmetry violation in nature and recent investigations on generalized uncertainty principle GUP models in anisotropic space, in this paper we identify GUP models satisfying two criteria i invariance of commutators under canonical transformations, and ii physical independence of position and momentum on the ordering of auxiliary operators in their definitions. Compliance of these criteria is fundamental if one wishes to unambiguously describe GUP using an algebraic approach but, surprisingly, neither is trivially satisfied when GUP is assumed within anisotropic space. As a consequence, we use these criteria to place important restrictions on what or how GUP models may be approached algebraically. |
AutoNMT A Framework to Streamline the Research of Seq2Seq Models ; We present AutoNMT, a framework to streamline the research of seqtoseq models by automating the data pipeline i.e., file management, data preprocessing, and exploratory analysis, automating experimentation in a toolkitagnostic manner, which allows users to use either their own models or existing seqtoseq toolkits such as Fairseq or OpenNMT, and finally, automating the report generation plots and summaries. Furthermore, this library comes with its own seqtoseq toolkit so that users can easily customize it for nonstandard tasks. |
Universal Guidance for Diffusion Models ; Typical diffusion models are trained to accept a particular form of conditioning, most commonly text, and cannot be conditioned on other modalities without retraining. In this work, we propose a universal guidance algorithm that enables diffusion models to be controlled by arbitrary guidance modalities without the need to retrain any usespecific components. We show that our algorithm successfully generates quality images with guidance functions including segmentation, face recognition, object detection, and classifier signals. Code is available at httpsgithub.comarpitbansal297UniversalGuidedDiffusion. |
Matrix product symmetries and breakdown of thermalization from hard rod deformations ; We construct families of exotic spin12 chains using a procedure called hard rod deformation''. We treat both integrable and nonintegrable examples. The models possess a large noncommutative symmetry algebra, which is generated by matrix product operators with fixed small bond dimension. The symmetries lead to Hilbert space fragmentation and to the breakdown of thermalization. As an effect, the models support persistent oscillations in nonequilibrium situations. Similar symmetries have been reported earlier in integrable models, but here we show that they also occur in nonintegrable cases. |
Experimental Study of a Parallel Iterative Solver for Markov Chain Modeling ; This paper presents the results of a preliminary experimental investigation of the performance of a stationary iterative method based on a block staircase splitting for solving singular systems of linear equations arising in Markov chain modelling. From the experiments presented, we can deduce that the method is well suited for solving block banded or more generally localized systems in a parallel computing environment. The parallel implementation has been benchmarked using several Markovian models. |
A Comparative Predicting Stock Prices using Heston and Geometric Brownian Motion Models ; This paper presents a novel approach to predicting stock prices using technical analysis. By utilizing Ito's lemma and EulerMaruyama methods, the researchers develop Heston and Geometric Brownian Motion models that take into account volatility, interest rate, and historical stock prices to generate predictions. The results of the study demonstrate that these models are effective in accurately predicting stock prices and outperform commonly used statistical indicators. The authors conclude that this technical analysisbased method offers a promising solution for stock market prediction. |
Switch Operators for the SixVertex Model ; In this paper, we introduce and analyze a new switch operator for the sixvertex model. This operator, derived from the YangBaxter equation, allows us to express the partition function with arbitrary boundaries in terms of a base case with domain wall boundary conditions. As an application, we derive explicit formulas for the factorial Schur functions and their generalizations. Our results provide new insights into the relationship between boundary conditions and partition functions in the sixvertex model. |
Multiscalar field cosmological model and possible solutions using Noether symmetry approach ; In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on one of the scalar fields. Instead of choosing these functions phenomenologically here, they are evaluated assuming the existence of Noether symmetry. By appropriate choice of a point transformation in the augmented space, one of the variables in the Lagrangian becomes cyclic and the evolution equations become much simpler to have solutions. Finally, the solutions are analyzed from cosmological view point. |
Conformal field theory, solitons, and elliptic CalogeroSutherland models ; We construct a nonchiral conformal field theory CFT on the torus that accommodates a second quantization of the elliptic CalogeroSutherland eCS model. We show that the CFT operator that provides this second quantization defines, at the same time, a quantum version of a soliton equation called the nonchiral intermediate longwave ncILW equation. We also show that this CFT operator is a second quantization of a generalized eCS model which can describe arbitrary numbers of four different kinds of particles; we propose that these particles can be identified with solitons of the quantum ncILW equation. |
The abuse of Open Source Code to Train Large Language Models ; In recent years, Large Language Models LLMs have gained significant popularity due to their ability to generate humanlike text and their potential applications in various fields, such as Software Engineering. LLMs for Code are commonly trained on large unsanitized corpora of source code scraped from the Internet. The content of these datasets is memorized and emitted by the models, often in a verbatim manner. In this work, we will discuss the security, privacy, and licensing implications of memorization. We argue why the use of copyleft code to train LLMs is a legal and ethical dilemma. Finally, we provide four actionable recommendations to address this issue. |
Learning highdimensional causal effect ; The scarcity of highdimensional causal inference datasets restricts the exploration of complex deep models. In this work, we propose a method to generate a synthetic causal dataset that is highdimensional. The synthetic data simulates a causal effect using the MNIST dataset with Bernoulli treatment values. This provides an opportunity to study varieties of models for causal effect estimation. We experiment on this dataset using Dragonnet architecture Shi et al. 2019 and modified architectures. We use the modified architectures to explore different types of initial Neural Network layers and observe that the modified architectures perform better in estimations. We observe that residual and transformer models estimate treatment effect very closely without the need for targeted regularization, introduced by Shi et al. 2019. |
Investigating the Translation Performance of a Large Multilingual Language Model the Case of BLOOM ; The NLP community recently saw the release of a new large openaccess multilingual language model, BLOOM BigScience et al., 2022 covering 46 languages. We focus on BLOOM's multilingual ability by evaluating its machine translation performance across several datasets WMT, Flores101 and DiaBLa and language pairs high and lowresourced. Our results show that 0shot performance suffers from overgeneration and generating in the wrong language, but this is greatly improved in the fewshot setting, with very good results for a number of language pairs. We study several aspects including prompt design, model sizes, crosslingual transfer and the use of discursive context. |
Inhomogeneous longrange percolation in the weak decay regime ; We study a general class of percolation models in Euclidean space including longrange percolation, scalefree percolation, the weightdependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which intercluster longrange connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the transience of infinite clusters. |
Randomized Symplectic Model Order Reduction for Hamiltonian Systems ; Simulations of large scale dynamical systems in multiquery or realtime contexts require efficient surrogate modelling techniques, as e.g. achieved via Model Order Reduction MOR. Recently, symplectic methods like the complex singular value decomposition cSVD or the SVDlike decomposition have been developed for preserving Hamiltonian structure during MOR. In the current contribution, we show how symplectic structure preserving basis generation can be made more efficient with randomized matrix factorizations. We present a randomized complex SVD rcSVD algorithm and a randomized SVDlike rSVDlike decomposition. We demonstrate the efficiency of the approaches with numerical experiments on high dimensional systems. |
Explainable Goal Recognition A Framework Based on Weight of Evidence ; We introduce and evaluate an eXplainable Goal Recognition XGR model that uses the Weight of Evidence WoE framework to explain goal recognition problems. Our model provides humancentered explanations that answer why and why not questions. We computationally evaluate the performance of our system over eight different domains. Using a human behavioral study to obtain the ground truth from human annotators, we further show that the XGR model can successfully generate humanlike explanations. We then report on a study with 60 participants who observe agents playing Sokoban game and then receive explanations of the goal recognition output. We investigate participants' understanding obtained by explanations through task prediction, explanation satisfaction, and trust. |
Theory of nonlinear whispering gallery mode dynamics in a cylindrical microresonator with a radius variation ; We propose a comprehensive model describing the Kerr nonlinear dynamics of an electric field in a cylindrical microresonator with an effective radius variation, coupled to a radiation source. The proposed system of equations for coupled azimuthal modes takes into account full azimuthal dispersion as well as the influence of the radiation source on the field in the microresonator with the coupling coefficients determined experimentally. The model appears a powerful tool to study nonlinear effects, generation axialazimuthal modes and optical frequency combs. We illustrate the power of the model with optimization of the coupling point of the light source, getting two order of magnitude improvement for the nonlinear threshold. |
On the duality between height functions and continuous spin models ; We revisit the classical phenomenon of duality between random integervalued height functions with positive definite potentials and abelian spin models with O2 symmetry. We use it to derive new results in quite high generality including a universal upper bound on the variance of the height function in terms of the Green's function a GFF bound which among others implies localisation on transient graphs; monotonicity of said variance with respect to a natural temperature parameter; the fact that delocalisation of the height function implies a BKT phase transition in planar models; and also delocalisation itself for height functions on periodic almost'' planar graphs. |
Bifurcation analysis of the Keynesian cross model ; This study rigorously investigates the Keynesian cross model of a national economy with a focus on the dynamic relationship between government spending and economic equilibrium. The model consists of two ordinary differential equations regarding the rate of change of national income and the rate of consumer spending. Three dynamic relationships between national income and government spending are studied. This study aims to classify the stabilities of equilibrium states for the economy by discussing different cases of government spending. Furthermore, the implication of government spending on the national economy is investigated based on phase portraits and bifurcation analysis of the dynamical system in each scenario. |
Signature flip in deceleration parameter A thermodynamic phase transition ; Using the HaywardKodama temperature for the apparent horizon, it is found that matter content in the Universe is not thermodynamically stable, and the entry to the late accelerated expansion is actually a second order phase transition. The cosmological model used for the purpose is one that imitates the LambdaCDM model, the favoured model for the present Universe. |
Properties of given and detected unbounded solutions to a class of chemotaxis models ; This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attractionrepulsion model, with nonlinear productions, diffusion, sensitivities and logistic term, we detect Lebesgue spaces where given unbounded solutions blowup also in the corresponding norms of those spaces; subsequently, estimates for the blowup time are established. Finally, for a simplified version of the model, some blowup criteria are proved. |
Adic tropicalizations and cofinality of Gubler models ; We introduce adic tropicalizations for subschemes of toric varieties as limits of Gubler models associated to polyhedral covers of the ordinary tropicalization. Our main result shows that Huber's adic analytification of a subscheme of a toric variety is naturally isomorphic to the inverse limit of its adic tropicalizations, in the category of locally topologically ringed spaces. The key new technical idea underlying this theorem is cofinality of Gubler models, which we prove for projective schemes and also for more general compact analytic domains in closed subschemes of toric varieties. In addition, we introduce a Gtopology and structure sheaf on ordinary tropicalizations, and show that Berkovich analytifications are limits of ordinary tropicalizations in the category of topologically ringed topoi. |
Exact Thermodynamics and Transport in the Classical SineGordon Model ; We revisit the exact thermodynamic description of the classical sineGordon field theory, a notorious integrable model. We found that existing results in the literature based on the solitongas picture did not correctly take into account light, but extended, solitons and thus led to incorrect results. This issue is regularized upon requantization we derive the correct thermodynamics by taking the semiclassical limit of the quantum model. Our results are then extended to transport settings by means of Generalized Hydrodynamics. |
WellPosedness and Polynomial energy decay rate of a transmission problem for Rayleigh beam model with heat conduction ; In this paper, we investigate the stability of the transmission problem for Rayleigh beam model with heat conduction. First, we reformulate our system into an evolution equation and prove our problem's wellposedness. Next, we demonstrate the resolvent of the operator is compact in the energy space, then by using the general criteria of ArendtBatty, we prove that the thermal dissipation is enough to stabilize our model. Finally, a polynomial energy decay rate has been obtained which depends on the mass densities and the moments of inertia of the Rayleigh beams. |
Inequality and Growth A TwoPlayer Dynamic Game with Production and Appropriation ; This paper models a twoagent economy with production and appropriation as a noncooperative dynamic game, and determines its closedform Markovian Nash equilibrium. The analysis highlights the parametric conditions that tip the economy from a nonaggressive or cooperative equilibrium to outright distributional conflict. The model includes parameters that capture the role of appropriation technology and destructiveness. The full dynamic implications of the game are yet to be explored, but the model offers a promising general framework for thinking about different technological and economic conditions as more or less conducive to cooperation or distributional conflict. |
Swarming models with specular boundary condition and environmental noise ; We investigate a general class of models for swarmingselfcollective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common environmental noise. We rigorously derive its corresponding macroscopic meanfield equation, which is a new type of stochastic partial differential equation due to the presence of common noise. The approach relies on a compactness argument, in which we first establish the tightness of the empirical measures associated with the particle system and then demonstrate that the time marginal of the limit measure is a solution to the meanfield equation. |
A NonLinear Type Equation of State and Cosmic Fluid Dynamics ; In this chapter we have introduced a special type of nonlinear equation of state to discuss the cosmological evolution mechanism. The new equation of state is a four parameters model which can be represented as pArhoBrho2fracCrhoalpha where BAbetagamma. The evolution of universe have been interpreted by fluid dynamics. The reconstruction of Chaplygin gas and VanDerWaals VDW fluid equation of states have been done from the parametric analysis of this new nonlinear model. Different cosmological phases like Quintom, Quintessence and warm universe have been discussed here. Finally, we have provided a comparative studies of this model with other nonlinear fluid solutions. |
Smart farming using iot for efficient crop growth ; In general. automated farming systems make decisions based on static models built from the properties of the plant. in the contrast, irrigation decisions in our suggested method are dynamically changing environmental conditions. the models learning process reveals the mathematical links between the environmental factors employed in the determining the irrigation habit and gradually improves its learning techniques as irrigation data accumulates int the model. to analyze overall system overall system performance, we constructed a test environment for the sensor edge, mobile client, and decision service in the cloud. |
Upcrossingrate dynamics for a minimal neuron model receiving spatially distributed synaptic drive ; The spatiotemporal stochastic dynamics of the voltage as well as the upcrossing rate are derived for a model neuron comprising a long dendrite with uniformly distributed filtered excitatory and inhibitory synaptic drive. A cascade of ordinary and partial differential equations is obtained describing the evolution of firstorder means and secondorder spatial covariances of the voltage and its rate of change. These quantities provide an analytical form for the general, steadystate and linear response of the upcrossing rate to dynamic synaptic input. It is demonstrated that this minimal dendritic model has an unexpectedly sustained highfrequency response despite synaptic, membrane and spatial filtering. |
Construction of coarsegrained molecular dynamics with manybody nonMarkovian memory ; We introduce a machinelearningbased coarsegrained molecular dynamics CGMD model that faithfully retains the manybody nature of the intermolecular dissipative interactions. Unlike common empirical CG models, the present model is constructed based on the MoriZwanzig formalism and naturally inherits the heterogeneous statedependent memory term rather than matching the meanfield metrics such as the velocity autocorrelation function. Numerical results show that preserving the manybody nature of the memory term is crucial for predicting the collective transport and diffusion processes, where empirical forms generally show limitations. |
DisjunctiveProgramming.jl Generalized Disjunctive Programming Models and Algorithms for JuMP ; We present a Julia package, DisjunctiveProgramming.jl, that extends the functionality in JuMP.jl to allow modeling problems via logical propositions and disjunctive constraints. Such models can then be reformulated into MixedInteger Programs MIPs that can be solved with the various MIP solvers supported by JuMP. To do so, logical propositions are converted to Conjunctive Normal Form CNF and reformulated into equivalent algebraic constraints. Disjunctions are reformulated into mixedinteger constraints via the reformulation technique specified by the user BigM or Hull reformulations. The package supports reformulations for disjunctions containing linear, quadratic, and nonlinear constraints. |
Attentionbased Part Assembly for 3D Volumetric Shape Modeling ; Modeling a 3D volumetric shape as an assembly of decomposed shape parts is much more challenging, but semantically more valuable than direct reconstruction from a full shape representation. The neural network needs to implicitly learn part relations coherently, which is typically performed by dedicated network layers that can generate transformation matrices for each part. In this paper, we propose a VoxAttention network architecture for attentionbased part assembly. We further propose a variant of using channelwise part attention and show the advantages of this approach. Experimental results show that our method outperforms most stateoftheart methods for the part relationaware 3D shape modeling task. |
The Role of AI in HumanAI Creative Writing for Hong Kong Secondary Students ; The recent advancement in Natural Language Processing NLP capability has led to the development of language models e.g., ChatGPT that is capable of generating humanlike language. In this study, we explore how language models can be utilized to help the ideation aspect of creative writing. Our empirical findings show that language models play different roles in helping student writers to be more creative, such as the role of a collaborator, a provocateur, etc |
Gauge fixing and gauge correlations in noncompact Abelian gauge models ; We investigate some general properties of linear gauge fixings and gaugefield correlators in lattice models with noncompact U1 gauge symmetry. In particular, we show that, even in the presence of a gauge fixing, some gaugefield observables like the photonmass operator are not welldefined, depending on the specific gauge fixing adopted and on its implementation. Numerical tests carried out in the threedimensional noncompact lattice Abelian Higgs model fully support the analytical results and provide further insights. |
Emergent U1 symmetry in nonparticleconserving 1D models ; The properties of stable Luttinger liquid phases in models with a nonconserved number of particles are investigated. We study the Luttinger liquid phases in onedimensional models of hardcore boson and spinless fermion chains where particles can be created and annihilated three by three on adjacent sites. We provide an intuitive and systematic method based on flow equations approach, which accounts for additional terms in the correlations generated by the mathbbZ3symmetric interactions. We find that despite the emergence of U1 symmetry under renormalization, the observables are still affected by its breaking in the bare Hamiltonian. In particular, the standard bosonization mapping becomes insufficient to capture the full behavior of correlation functions. |
Conformal Nucleus Sampling ; Language models generate text based on successively sampling the next word. A decoding procedure based on nucleus topp sampling chooses from the smallest possible set of words whose cumulative probability exceeds the probability p. In this work, we assess whether a topp set is indeed aligned with its probabilistic meaning in various linguistic contexts. We employ conformal prediction, a calibration procedure that focuses on the construction of minimal prediction sets according to a desired confidence level, to calibrate the parameter p as a function of the entropy of the next word distribution. We find that OPT models are overconfident, and that calibration shows a moderate inverse scaling with model size. |
Characterization of realanalytic infinitesimal CR automorphisms for a class of hypersurfaces in Bbb C4. ; In this paper, motivated by the work of Kim and Kolar for the case of pseudoconvex models which are sums of squares of polynomials, we study the Lie algebra of realanalytic infinitesimal CR automorphisms of a model hypersurface M0 given by beginequation M0 z,w in mathbb C3 times mathbb C Im w Pbar Q Qbar P Rbar R , endequation where P, Q and R are homogeneous polynomials. In particular, we classify M0 with respect to the description of its nilpotent rotations when P, Q and R are monomials. We also give an example of a model M0 for which the real dimension of its generalized exotic rotations is 3. |
Power Grid Transient Analysis via OpenSource Circuit Simulator A Case Study of HVDC ; This paper proposes an electronic circuit simulatorbased method to accelerate the power system transient simulation, where the modeling of a generic HVDC High Voltage Direct Current system is focused. The electronic circuit simulation equations and the backward differentiation formula for numerical solving are described. Then, the circuit modeling process for power system components such as slack bus, constant power load, and HVDC are respectively illustrated. Finally, a case study is conducted on a fourbus power system to demonstrate the effectiveness of the proposed modeling and simulation method. |
Jet Diffusion versus JetGPT Modern Networks for the LHC ; We introduce two diffusion models and an autoregressive transformer for LHC physics simulations. Bayesian versions allow us to control the networks and capture training uncertainties. After illustrating their different density estimation methods for simple toy models, we discuss their advantages for Z plus jets event generation. While diffusion networks excel through their precision, the transformer scales best with the phase space dimensionality. Given the different training and evaluation speed, we expect LHC physics to benefit from dedicated use cases for normalizing flows, diffusion models, and autoregressive transformers. |
When SAM Meets Shadow Detection ; As a promptable generic object segmentation model, segment anything model SAM has recently attracted significant attention, and also demonstrates its powerful performance. Nevertheless, it still meets its Waterloo when encountering several tasks, e.g., medical image segmentation, camouflaged object detection, etc. In this report, we try SAM on an unexplored popular task shadow detection. Specifically, four benchmarks were chosen and evaluated with widely used metrics. The experimental results show that the performance for shadow detection using SAM is not satisfactory, especially when comparing with the elaborate models. Code is available at httpsgithub.comLeipingJieSAMSh. |
Natural coordinates and horizontal approximations in twofield cosmological models ; We construct natural local coordinate systems on the phase space of twofield cosmological models with orientable target space, which allow for a description of cosmological flows through quantities of direct physical interest. Such coordinates are induced by the fundamental observables of the model, which we formulate geometrically using the tautological bundle of the tangent bundle of the scalar manifold. We also describe a large class of geometric dynamical approximations induced by the choice of an Ehresmann connection in the tangent bundle of the scalar manifold. Such approximations take a conceptually simple form in natural coordinates and we illustrate one of them as an application. |
Improving Isochronous Machine Translation with Target Factors and Auxiliary Counters ; To translate speech for automatic dubbing, machine translation needs to be isochronous, i.e. translated speech needs to be aligned with the source in terms of speech durations. We introduce target factors in a transformer model to predict durations jointly with target language phoneme sequences. We also introduce auxiliary counters to help the decoder to keep track of the timing information while generating target phonemes. We show that our model improves translation quality and isochrony compared to previous work where the translation model is instead trained to predict interleaved sequences of phonemes and durations. |
Can Large Language Models Infer and Disagree Like Humans ; Large Language Models LLMs have shown stellar achievements in solving a broad range of tasks. When generating text, it is common to sample tokens from these models whether LLMs closely align with the human disagreement distribution has not been wellstudied, especially within the scope of Natural Language Inference NLI. In this paper, we evaluate the performance and alignment of LLM distribution with humans using two different techniques Monte Carlo Reconstruction MCR and Log Probability Reconstruction LPR. As a result, we show LLMs exhibit limited ability in solving NLI tasks and simultaneously fail to capture human disagreement distribution, raising concerns about their natural language understanding NLU ability and their representativeness of human users. |
The Quadratic Local Variance Gamma Model an arbitragefree interpolation of class mathcalC3 for option prices ; This paper generalizes the local variance gamma model of Carr and Nadtochiy, to a piecewise quadratic local variance function. The formulation encompasses the piecewise linear Bachelier and piecewise linear Black local variance gamma models. The quadratic local variance function results in an arbitragefree interpolation of class mathcalC3. The increased smoothness over the piecewiseconstant and piecewiselinear representation allows to reduce the number of knots when interpolating raw market quotes, thus providing an interesting alternative to regularization while reducing the computational cost. |
Initialboundary value problems for Poiseuille flow of nematic liquid crystal via full EricksenLeslie model ; In this paper, we study the initialboundary value problem for the Poiseuille flow of hyperbolicparabolic EricksenLeslie model of nematic liquid crystals in one space dimension. Due to the quasilinearity, the solution of this model in general forms cusp singularity. We prove the global existence of Holder continuous solution, which may include cusp singularity, for initialboundary value problems with different types of boundary conditions. |
SecondOrder Hyperproperties ; We introduce Hyper2LTL, a temporal logic for the specification of hyperproperties that allows for secondorder quantification over sets of traces. Unlike firstorder temporal logics for hyperproperties, such as HyperLTL, Hyper2LTL can express complex epistemic properties like common knowledge, Mazurkiewicz trace theory, and asynchronous hyperproperties. The model checking problem of Hyper2LTL is, in general, undecidable. For the expressive fragment where secondorder quantification is restricted to smallest and largest sets, we present an approximate modelchecking algorithm that computes increasingly precise under and overapproximations of the quantified sets, based on fixpoint iteration and automata learning. We report on encouraging experimental results with our modelchecking algorithm, which we implemented in the tooltextttHySO. |
The Stratified Foundations as a theory modulo ; The Stratified Foundations are a restriction of naive set theory where the comprehension scheme is restricted to stratifiable propositions. It is known that this theory is consistent and that proofs strongly normalize in this theory. Deduction modulo is a formulation of firstorder logic with a general notion of cut. It is known that proofs normalize in a theory modulo if it has some kind of manyvalued model called a premodel. We show in this paper that the Stratified Foundations can be presented in deduction modulo and that the method used in the original normalization proof can be adapted to construct a premodel for this theory. |
The Uniqueness of the GinzburgRallis Model the NonArchimedean Case ; We prove the uniqueness of the GinzburgRallis models over padic local fields of characteristic zero, which completes the local uniqueness problem for the GinzburgRallis models starting from the work of C.F. Nien in citeMR2709083 that proves the nonsplit case, and the work of D. Jiang, B. Sun and C. Zhu in citeMR2763736 that proves the general case over Archimedean local fields. Our proof extends the strategy of citeMR2763736 to the padic case with the help of the refined structure of the wavefront sets of mathfrak zfinite distributions as developed by A. Aizenbud, D. Gourevitch and E. Sayag in citeMR3406530. |
Is the background evolution of CDM model consistent with observations ; We establish a new and cosmologicalmodelindependent method to explore the cosmic background dynamics in this work. Utilizing the latest Pantheon type Ia supernova sample and the Hubble parameter measurements, we obtain the values of the Hubble parameter and the deceleration parameter at five different redshift points ranging from 0.2 to 0.6, and find that they can deviate from the predictions of the LambdaCDM model at more than 2sigma. We further probe the equation of state of dark energy and obtain that a slightly oscillating equation of state of dark energy around the 1 line is favored. |
Percolation and topological properties of temporal higherorder networks ; Many timevarying networks exhibit nonpairwise interactions that cannot be effectively captured by traditional graph models. Here, we propose a hidden variables formalism to analytically characterize higherorder temporal networks. We apply our framework to a higherorder activitydriven model, providing analytical expressions for the main topological properties of the timeintegrated hypergraphs, depending on the integration time and the activity distributions characterizing the model. Furthermore, we provide analytical estimates for the percolation times of general classes of uncorrelated and correlated hypergraphs. Finally, we quantify the extent to which the percolation threshold of empirical social interactions is underestimated when their higherorder nature is neglected. |
Improving Grammarbased SequencetoSequence Modeling with Decomposition and Constraints ; Neural QCFG is a grammarbased sequencetosequence seq2seq model with strong inductive biases on hierarchical structures. It excels in interpretability and generalization but suffers from expensive inference. In this paper, we study two lowrank variants of Neural QCFG for faster inference with different tradeoffs between efficiency and expressiveness. Furthermore, utilizing the symbolic interface provided by the grammar, we introduce two soft constraints over tree hierarchy and source coverage. We experiment with various datasets and find that our models outperform vanilla Neural QCFG in most settings. |
Holography for cylindrical gravitational waves ; We study a two dimensional nonlinear sigma model whose classical solutions describe cylindrical gravitational wave scattering with zero cosmological constant. We quantize this sigma model and compute its twoparticle treelevel Smatrix. We discuss an SL2,R symmetry of the sigma model called the Ehlers group and directly verify the associated Smatrix conservation law at tree level. Finally, we use the holographic dictionary to define a dual boundary theory and compute its twopoint correlation function. This is an example of holography with zero cosmological constant. |
On the Quantum Theory of 3 Dimensional de Sitter Space ; We sketch the construction of a quantum model of 3 dimensional de Sitter space, based on the Covariant Entropy Principle and the observation that semiclassical physics suggests the possibility of a consistent theory of a finite number of unstable massive particles with purely gravitational interactions. Our model is holographic, finite, unitary, causal, plausibly exhibits fast scrambling, and qualitatively reproduces features of semiclassical de Sitter physics. In an appendix we outline some calculations that might lead to further tests of the model. |
Measuring Sentiment Bias in Machine Translation ; Biases induced to text by generative models have become an increasingly large topic in recent years. In this paper we explore how machine translation might introduce a bias in sentiments as classified by sentiment analysis models. For this, we compare three open access machine translation models for five different languages on two parallel corpora to test if the translation process causes a shift in sentiment classes recognized in the texts. Though our statistic test indicate shifts in the label probability distributions, we find none that appears consistent enough to assume a bias induced by the translation process. |
Large deviation properties for pattern statistics in primitive rational models ; We present a large deviation property for the pattern statistics representing the number of occurrences of a symbol in words of given length generated at random according to a rational stochastic model. The result is obtained assuming that in the model the overall weighted transition matrix is primitive. In particular we obtain a rate function depending on the main eigenvalue and eigenvectors of that matrix. Under rather mild conditions, we show that the range of validity of our large deviation estimate can be extended to the interval 0,1, which represents in our context the largest possible open interval of validity of the property. |
Black Hole Mergers in Holographic Spacetime HST Models of Inflation ; We perform a crude computer simulation to show that no problematic black holes are formed by mergers in the early matter dominated phase of the HST models of inflation. These are black holes whose decays could have been seen as signals in the CMB. We also conclude that tiny black hole galaxies form. Since black hole decay products are mostly massive standard model particles, and perhaps their superpartners, the fate of these protogalaxies is a complicated dynamical problem. |
Isinglike models on Euclidean black holes ; We study spin models on Euclidean black hole backgrounds. These resemble the Ising model, but are inhomogeneous with two parameters, the black hole mass and the cosmological constant. We use MonteCarlo methods to study macroscopic properties of these systems for Schwarzschild and antideSitter black holes in four and five dimensions for spin12 and spin1. We find in every case that increasing the black hole mass causes the spins to undergo a second order phase transition from disorder to order and that the phase transition occurs at subPlanckian black hole mass. |
Dynamics of squirmers in explicitly modeled polymeric fluids ; Biological microswimmers such as bacteria and sperm cells often encounter complex biological fluid environments. Here we use the wellknown squirmer microswimmer model to show the importance of the local fluid microstructure and noncontinuum effects on their swimming speed in different polymeric and filamentous fluids. Surprisingly, we find that different squirmer types move at considerably different speed in filamentous fluids which cannot be explained by existing continuum models, but by considering the local fluid and polymer properties around the squirmers. Furthermore, direct squirmerpolymer interactions slow down in particular pushers by trapping large stiff filaments in a selfgenerated recirculation region in front of them. |
Accelerating Plane Symmetric Cosmological Model with Bulk Viscous and Cosmic Strings in Lyra's Geometry ; The present study deals with Lyra's geometry in plane symmetric metric discussed in the presence of bulk viscous fluid and one dimensional strings are assumed to be loaded with particles and the particle energy density. The variation of Hubble's parameter gives a constant value of decelerating parameter. The exact solution has been found for the plane symmetric model in Lyra's geometry in the framework of bulk viscosity and string cosmology. Also, the bulk viscous pressure is assumed to be proportional to the energy density. The physical and geometrical properties of the model are also discussed. |
An exact model of a gravitational wave in the Bianchi III universe based on Shapovalov II wave spacetime and the quadratic theory of gravity ; Exact models of primordial gravitational waves in the Bianchi type III universe are constructed on the basis of the quadratic theory of gravity with a scalar field and pure radiation in Shapovalov wave spacetimes of type II subtype 2. Exact solutions of field equations and scalar equation are obtained. The characteristics of pure radiation are determined. An explicit form of the scalar field functions included in the Lagrangian of the considered quadratic theory of gravity is found. Trajectories of propagation of light rays in the considered gravitationalwave models are obtained. |
Iterated Piecewise Affine IPA Approximation for Language Modeling ; In this work, we demonstrate the application of a simple firstorder Taylor expansion to approximate a generic function F Rn times m to Rn times m and utilize it in language modeling. To enhance the basic Taylor expansion, we introduce iteration and piecewise modeling, leading us to name the algorithm the Iterative Piecewise Affine IPA approximation. The final algorithm exhibits interesting resemblances to the Transformers decoder architecture. By comparing parameter arrangements in IPA and Transformers, we observe a strikingly similar performance, with IPA outperforming Transformers by 1.5 in the next token prediction task with crossentropy loss for smaller sequence lengths. |
Treelevel UV completions for NRSMEFT d6 and d7 operators ; We study ultraviolet completions for operators in standard model effective field theory extended with righthanded neutrinos NRSMEFT. Using a diagrammatic method, we generate systematically lists of possible treelevel completions involving scalars, fermions or vectors for all operators at d6 and d7, which contain at least one righthanded neutrino. We compare our lists of possible UV models to the ones found for pure SMEFT. We also discuss how the observation of LNV processes via NRSMEFT operators at the LHC can be related to Majorana neutrino masses of the standard model neutrinos. |
Tracking public attitudes toward ChatGPT on Twitter using sentiment analysis and topic modeling ; ChatGPT sets a new record with the fastestgrowing user base, as a chatbot powered by a large language model LLM. While it demonstrates stateoftheart capabilities in a variety of languagegenerating tasks, it also raises widespread public concerns regarding its societal impact. In this paper, we utilize natural language processing approaches to investigate the public attitudes towards ChatGPT by applying sentiment analysis and topic modeling techniques to Twitter data. Our result shows that the overall sentiment is largely neutral to positive, which also holds true across different occupation groups. Among a wide range of topics mentioned in tweets, the most popular topics are Artificial Intelligence, Search Engines, Education, Writing, and Question Answering. |
Sketching a Model on Fisheries Enforcement and Compliance A Survey ; Monitoring and enforcement considerations have been largely forgotten in the study of fishery management. This paper discusses this issue through a model formalization to show the impacts of costly, imperfect enforcement of law on the behavior of fishing firms and fisheries management. Theoretical analysis merges a standard bioeconomic model of fisheries GordonSchaefer with Becker theory of Crime and Punishment. |
Infinite affine, hyperbolic and Lorentzian Weyl groups with their associated Calogero models ; We propose generalizations of Calogero models that exhibit invariance with respect to the infinite Weyl groups of affine, hyperbolic, and Lorentzian types. Our approach involves deriving closed analytic formulas for the action of the associated Coxeter elements of infinite order acting on arbitrary roots within their respective root spaces. These formulas are then utilized in formulating the new type of Calogero models. |
Computational complexity of kstable matchings ; We study deviations by a group of agents in the three main types of matching markets the house allocation, the marriage, and the roommates models. For a given instance, we call a matching kstable if no other matching exists that is more beneficial to at least k out of the n agents. The concept generalizes the recently studied majority stability. We prove that whereas the verification of kstability for a given matching is polynomialtime solvable in all three models, the complexity of deciding whether a kstable matching exists depends on frackn and is characteristic to each model. |
Identification in Multiple Treatment Models under Discrete Variation ; We develop a method to learn about treatment effects in multiple treatment models with discretevalued instruments. We allow selection into treatment to be governed by a general class of threshold crossing models that permits multidimensional unobserved heterogeneity. Under a semiparametric restriction on the distribution of unobserved heterogeneity, we show how a sequence of linear programs can be used to compute sharp bounds for a number of treatment effect parameters when the marginal treatment response functions underlying them remain nonparametric or are additionally parameterized. |
An infty,ncategorical straighteningunstraightening construction ; We provide an infty,ncategorical version of the straighteningunstraightening construction, asserting an equivalence between the infty,ncategory of double infty,n1right fibrations over an infty,ncategory mathcalC and that of the infty,nfunctors from mathcalC valued in infty,n1categories. We realize this in the form of a Quillen equivalence between appropriate model structures; on the one hand, a model structure for double infty,n1right fibrations over a generic precategory object W in infty,n1categories and, on the other hand, a model structure for infty,nfunctors from its homotopy coherent categorification mathfrakC W valued in infty,n1categories. |
Large Language Models Perform Diagnostic Reasoning ; We explore the extension of chainofthought CoT prompting to medical reasoning for the task of automatic diagnosis. Motivated by doctors' underlying reasoning process, we present DiagnosticReasoning CoT DRCoT. Empirical results demonstrate that by simply prompting large language models trained only on general text corpus with two DRCoT exemplars, the diagnostic accuracy improves by 15 comparing to standard prompting. Moreover, the gap reaches a pronounced 18 in outdomain settings. Our findings suggest expertknowledge reasoning in large language models can be elicited through proper promptings. |
Statistical Mobility of Multicellular Colonies of Flagellated Swimming Cells ; We study the stochastic hydrodynamics of colonies of flagellated swimming cells, typified by multicellular choanoflagellates, which can form both rosette and chainlike shapes. The objective is to link cellscale dynamics to colonyscale dynamics for various colonial morphologies. Via autoregressive stochastic models for the cycleaveraged flagellar force dynamics and statistical models for demographic celltocell variability in flagellar properties and placement, we derive effective transport properties of the colonies, including celltocell variability. We provide the most quantitative detail on disclike geometries to model rosettes, but also present formulas for the dynamics of general planar colony morphologies, which includes planar chainlike configurations. |
A Heavy QCD Axion model in Light of Pulsar Timing Arrays ; Recently, pulsar timing array PTA experiments reported the observation of a stochastic gravitational wave GW background in the nanohertz range frequency band. We show that such signal can be originated from a cosmological firstorder phase transition PT within a wellmotivated heavy visible QCD axion model. Considering the PecceiQuinn symmetry breaking at the TeV scale in the scenario, we find a supercooled PT, in the parameter space of the model, prolonging the PT with the reheating temperature at the GeV scale. |
SPICE Modeling of Memcomputing Logic Gates ; Memcomputing logic gates generalize the traditional Boolean logic gates for operation in the reverse direction. According to the literature, this functionality enables the efficient solution of computationallyintensive problems including factorization and NPcomplete problems. To approach the deployment of memcomputing gates in hardware, this paper introduces SPICE models of memcomputing logic gates following their original definition. Using these models, we demonstrate the behavior of single gates as well as small selforganizing circuits. We also correct some inconsistencies in the prior literature. Importantly, the correct schematics of dynamic correction module is reported here for the first time. Our work makes memcomputing more accessible to those who are interested in this emerging computing technology. |
Online Stochastic Allocation of Reusable Resources ; We study a multiobjective model on the allocation of reusable resources under model uncertainty. Heterogeneous customers arrive sequentially according to a latent stochastic process, request for certain amounts of resources, and occupy them for random durations of time. The decision maker's goal is to simultaneously maximize multiple types of rewards generated by the customers, while satisfying the resource capacity constraints in each time step. We develop models and algorithms for deciding on the allocation actions. We show that when the usage duration is relatively small compared with the length of the planning horizon, our policy achieves 1Oepsilon fraction of the optimal expected rewards, where epsilon decays to zero at a near optimal rate as the resource capacities grow. |
Absorption of Fermionic Dark Matter via the Scalar Portal ; The absorption of fermionic dark matter has recently been studied as a signature for the direct detection of dark matter. We construct the first UV completion of the scalar effective operator associated with this signature. We calculate the constraints on the model and demonstrate there is viable parameter space which can be probed by a nextgeneration experiment such as XLZD. We also consider the cosmological history of our model and show that the correct relic abundance can be obtained via freezeout in the dark sector. However, within this minimal model, we find that the absorption signal is highly suppressed in the parameter space that yields the correct relic abundance. |
Evolution of Gravitational Waves in Nonminimal Coupling Between Geometry and Matter Theories of Gravity ; We consider some specific models of nonminimal mattergeometry coupling theories and investigate the propagation of the gravitational waves in them. Extracting the temporal evolution of the gravitational wave equation within the framework of a flat FRW universe with a perfect fluid distribution, we analyze the waveforms traveling during the time. We find that while both the amplitude and frequency of the GWs decay with time in all considered models, the rate of reduction is highly sensitive to the values of the equation of state parameter and input parameters of the considered models. |
ReferenceFree Isotropic 3D EM Reconstruction using Diffusion Models ; Electron microscopy EM images exhibit anisotropic axial resolution due to the characteristics inherent to the imaging modality, presenting challenges in analysis and downstream tasks.In this paper, we propose a diffusionmodelbased framework that overcomes the limitations of requiring reference data or prior knowledge about the degradation process. Our approach utilizes 2D diffusion models to consistently reconstruct 3D volumes and is wellsuited for highly downsampled data. Extensive experiments conducted on two public datasets demonstrate the robustness and superiority of leveraging the generative prior compared to supervised learning methods. Additionally, we demonstrate our method's feasibility for selfsupervised reconstruction, which can restore a single anisotropic volume without any training data. |
A Review of Change of Variable Formulas for Generative Modeling ; Changeofvariables CoV formulas allow to reduce complicated probability densities to simpler ones by a learned transformation with tractable Jacobian determinant. They are thus powerful tools for maximumlikelihood learning, Bayesian inference, outlier detection, model selection, etc. CoV formulas have been derived for a large variety of model types, but this information is scattered over many separate works. We present a systematic treatment from the unifying perspective of encoderdecoder architectures, which collects 28 CoV formulas in a single place, reveals interesting relationships between seemingly diverse methods, emphasizes important distinctions that are not always clear in the literature, and identifies surprising gaps for future research. |
On the Vessel Energy Requirement Prediction From the Acceleration Stage Towing Experiments on Models ; One of the most crucial tasks for naval architects is computing the energy required to meet the ship's operational needs. When predicting a ship's energy requirements, a series of resistance tests on a scaled model vessel is carried out in the constant speed stage. Another important component is the ship's hydrodynamic added mass, which should also be considered when performing the seakeeping analysis. The second law of dynamics states that all this information, that is, the hull resistance dependence on the vessel's speed and the added mass, is accessible from just one acceleration stage towing test done up to the maximal speed. Therefore, this work aims to generalize Froude's scaling procedure from the model to fullscale vessels for accelerated motion. |
Sampling and Filtering with Markov Chains ; A continuoustime Markov chain rate change formula for simulation, model selection, filtering and theory is proven. It is used to develop Markov chain importance sampling, rejection sampling, branching particle filtering algorithms and filtering equations akin to the DuncanMortensenZakai equation and the FujisakiKallianpurKunita equation but for Markov signals with general continuoustime Markov chain observations. A direct method of solving these filtering equations is given that, for example, applies to trend, volatility andor parameter estimation in financial models given tickbytick market data. All the results also apply to continuoustime Hidden Markov Models CTHMM, which have become important in applications like disease progression tracking, as special cases and the corresponding CTHMM results are stated as corollaries. |
New dualityinvariant models for nonlinear supersymmetric electrodynamics ; We propose a new family of mathsfU1 dualityinvariant models for nonlinear cal N1 supersymmetric electrodynamics coupled to supergravity. This family includes the CribioriFarakosTournoyvan Proeyen supergravitymatter theory for spontaneously broken local supersymmetry with a novel FayetIliopoulos term without gauged Rsymmetry. We present superconformal dualityinvariant models. |
OCDaf Ordered Causal Discovery with Autoregressive Flows ; We propose OCDaf, a novel orderbased method for learning causal graphs from observational data. We establish the identifiability of causal graphs within multivariate heteroscedastic noise models, a generalization of additive noise models that allow for nonconstant noise variances. Drawing upon the structural similarities between these models and affine autoregressive normalizing flows, we introduce a continuous search algorithm to find causal structures. Our experiments demonstrate stateoftheart performance across the Sachs and SynTReN benchmarks in Structural Hamming Distance SHD and Structural Intervention Distance SID. Furthermore, we validate our identifiability theory across various parametric and nonparametric synthetic datasets and showcase superior performance compared to existing baselines. |
Misspecified BernsteinVon Mises theorem for hierarchical models ; We derive a Bernstein vonMises theorem in the context of misspecified, noni.i.d., hierarchical models parametrized by a finitedimensional parameter of interest. We apply our results to hierarchical models containing nonlinear operators, including the squared integral operator, and PDEconstrained inverse problems. More specifically, we consider the elliptic, timeindependent Schrodinger equation with parametric boundary condition and general parabolic PDEs with parametric potential and boundary constraints. Our theoretical results are complemented with numerical analysis on synthetic data sets, considering both the square integral operator and the Schrodinger equation. |
Differentiable Robust Model Predictive Control ; Deterministic model predictive control MPC, while powerful, is often insufficient for effectively controlling autonomous systems in the realworld. Factors such as environmental noise and model error can cause deviations from the expected nominal performance. Robust MPC algorithms aim to bridge this gap between deterministic and uncertain control. However, these methods are often excessively difficult to tune for robustness due to the nonlinear and nonintuitive effects that controller parameters have on performance. To address this challenge, a unifying perspective on differentiable optimization for control is presented, which enables derivation of a general, differentiable tubebased MPC algorithm. The proposed approach facilitates the automatic and realtime tuning of robust controllers in the presence of large uncertainties and disturbances. |
Continuum model of strong lightmatter coupling for molecular polaritons ; Strong coupling between light and matter generates hybrid polaritons. We present a continuum model that describes the polaritons by light and matter densities of states DOS that only depend on the refractive index of the material. This model is applied to molecular polaritons derived from molecules with broad spectral absorption. While the photonic DOS has a complex spectral distribution, the matter DOS is largely unmodified by strong coupling. We argue that bright states cannot be partitioned from dark states, and instead the photonic DOS is shared over a vast number of matter states. |
Student't mixture models for stock indices. A comparative study ; We perform a comparative study for multiple equity indices of different countries using different models to determine the best fit using the KolmogorovSmirnov statistic, the AndersonDarling statistic, the Akaike information criterion and the Bayesian information criteria as goodnessoffit measures. We fit models both to daily and to hourly logreturns. The main result is the excellent performance of a mixture of three Student's t distributions with the numbers of degrees of freedom fixed a priori 3St. In addition, we find that the different components of the 3St mixture with smallmoderatehigh degree of freedom parameter describe the extrememoderatesmall logreturns of the studied equity indices. |
Parabolic Anderson model with colored noise on torus ; We construct an intrinsic family of Gaussian noises on ddimensional flat torus mathbbTd. It is the analogue of the colored noise on mathbbRd, and allows us to study stochastic PDEs on torus in the Ito sense in high dimensions. With this noise, we consider the parabolic Anderson model PAM with measurevalued initial conditions and establish some basic properties of the solution, including a sharp upper and lower bound for the moments and Holder continuity in space and time. The study of the toy model of mathbbTd in the present paper is a first step towards our effort in understanding how geometry and topology play an role in the behavior of stochastic PDEs on general compact manifolds. |
PeriodDoubling Route to Chaos and Intermittency in a Hybrid Rossler Model ; A Rossler model perturbed with a piecewise constant function is investigated. The perturbation function used in the model is constructed by means of the logistic map. In the absence of the perturbation the system is assumed to possess two equilibrium points one of which is linearly stable. The occurrences of perioddoubling cascade and intermittency are numerically investigated. Extensions of the aforementioned phenomena among coupled Rossler systems are also shown. Our results reveal that discontinuous perturbations are capable of generating continuous chaos. |